Mathematics is a method of logic.

Mathematics is the art of giving the same name to different things.

Mathematics is a language plus reasoning; it is like a language plus logic. Mathematics is a tool for reasoning.

Mathematics is the science which draws necessary conclusions.

Mathematics consists in proving the most obvious thing in the least obvious way.

Mathematics, you see, is not a spectator sport. To understand mathematics means to be able to do mathematics. And what does it mean [to be] doing mathematics? In the first place, it means to be able to solve mathematical problems.

Mathematics is principally a tool to meditate, rather than to compute.

Mathematics is not a science from our point of view, in the sense that it is not a natural science. The test of its validity is not experiment.

Pure mathematics consists entirely of assertions to the effect that, if such and such a proposition is true of anything, then such and such another proposition is true of that thing. It is essential not to discuss whether the first proposition is really true, and not to mention what the anything is, of which it is supposed to be true. [...] Thus mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true. People who have been puzzled by the beginnings of mathematics will, I hope, find comfort in this definition, and will probably agree that it is accurate.

Mathematics is only a tool and one should learn to hold the physical ideas in one's mind without reference to the mathematical form.

Math is not thinking. Math is procedure. Memory is not thinking. Memory is storage. Thinking is thinking. Problem, solution. You and me think same speed. Why, question?

Mathematics is not a science from our point of view, in the sense that it is not a natural science. The test of its validity is not experiment. We must, incidentally, make it clear from the beginning that if a thing is not a science, it is not necessarily bad. For example, love is not a science. So, if something is said not to be a science, it does not mean that there is something wrong with it; it just means that it is not a science.

Mathematics has a threefold purpose. It must provide an instrument for the study of nature. But this is not all: it has a philosophical purpose, and, I daresay, an aesthetic purpose.

"Mathematics is not just a "numbers game", it is a way of thinking."